I am making a music video that actually has a budget and I came up with a total of 5400 figuring in a DP, Lights, Steadycam, etc and gave the client a detailed budget of what the things are going to cost to add up to 5400.00

When I made the budget I figured in a little extra for the crew parts just to be sure that I can have it covered.

So for example on the budget I put down 500 for makeup. And lets say I get a makeup person for 400.00 & I get lighting for 700 instead of a 1000.00

And lets say the client ask or finds out the EXACT amount I spent for the lighting or makeup. What do you say or do? I am not trying to rip anyone off. but there are also things that I will spend money on that I did not write in the budget like food, gas, travel, & an VFX person for one shot.

Should I just explain that yes it is lower than the budget but there are things I did not account for?

Don't explain anything. when you get your washing machine fixed, they tell you how much the labour is and the new pump is 55 - the customer doesn't ask if you actually paid 55 for the pump, they accept there's a markup.

As you say, you will obviously forget some things, and if you state 400 for the makeup artiste, but actually pay them 350, so what? It's business. If they like your end figure, then why would they try to generate their own quote? If they could do that, and had the skills and contacts, then they would have done it themselves. If they OK your quote, then your individual costings are none of their business.

Very Nice Thank You

I wouldn't worry about it Dave...people in business already know these things well enough. The ones who ask can be reminded that they don't sell their products on cost, so why should you?